Sherin's disappearance has transfixed the Dallas area. Her father told investigators that he looked outside 15 minutes after he sent Sherin into the alley but she was gone, according to police affidavits.
Not yet too worried, the father said, he then did a load of laundry, according to the affidavit. He waited until after sunrise before he reported the disappearance to police.
Detectives and FBI agents searched Mathews's house midweek and subsequently announced that someone left in the family's SUV about 4 am the day she disappeared and returned home within the hour.
Police said Sherin's mother was asleep during the incident and has not been charged, but the station reported that she also has stopped cooperating.
Police scoured Richardson, a suburb of 100,000 about 24km north of Dallas. They brought in search dogs, flew over Sherin's neighbourhood in helicopters and canvassed door to door for the girl last seen wearing a pink top, black pyjama bottoms and pink flip flops.
Mathews and his wife, Sini, adopted Sherin about two years ago from an orphanage in India, said Sergeant Kevin Perlich, a spokesman for the Richardson Police Department.
Mathews told police that Sherin was malnourished and had to be on a special diet to gain weight. She had to be fed whenever she was awake, Perlich said, and wasn't cooperating when her father tried to feed her.
"So that was the frustration [Mathews] was experiencing that night," Perlich said. "But, of course, we're working to verify all of that."